Authenticator needs an option to change the default sorting order of its entries. AFAICS it shows items in random order, which just makes it harder to find the desired code (I know there is a search button, but it shouldn’t be needed every time).
Also, please add site icons (already supported on the TOTP section of Password Manager), it would greatly help locating the needed entry.
And, finally, please consider adding a card layout, similar to Authy’s (in this case, icons are mandatory 
)
Bonus tip: on the Android app, showing a toast message for a couple of seconds indicating the code has been copied to the clipboard would be helpful (both on Authenticator and Password Manager)